Comparing med school acceptance rates is a tricky business.
First of all, you’re talking about two schools with a different range of student achievement upon entry, so you’d expect the acceptance rates to differ just based on that pre-filter; but that doesn’t mean comparable students at each school fare any differently.
Secondly, without digging much deeper, you cannot know how much the premed field at either school is winnowed down, through “weeder” courses and through the particular school’s policy about providing the all-important endorsement for med school applications. (Some schools have very high med school acceptance rates because they won’t endorse any but the most qualified candidates. The actual ratio of accepted students to those who wanted to apply can be much, much lower.)
Given how these factors vary, that one number (while it may sound great) is a terrible way of comparing whether one specific student (i.e. you) would have a better shot at med school via one college vs. another. It’s entirely possible that you-in-particular would have better odds at Auburn than at UNC, if being closer to the top of that particular talent pool would improve your chances of a stellar GPA. Then again, that’s not a foregone conclusion. (Competitive admissions do not always correlate with tougher grading curves.) All I’m saying is that you have to dig a lot deeper. I don’t necessarily disagree with your mom about the opportunities at Chapel Hill - as a parent, I would feel dubious about paying more for the sports-fan experience over top-tier academics, and it’s not even as if the Tar Heels are unworthy of fandom. But I don’t think she should be hung up on the med school acceptance rate specifically. And sometimes “fit” and “vibe” can be more important than “rank.” (The question is, if in fact you’re right about being happier at Auburn, would it be the happiness-begets-success kind of happiness, or the having-too-much-fun-to-worry-about-success kind of happiness?)
Also, as others have asked, how close in cost is “a good bit closer,” exactly…? What program/major are you accepted to at Auburn? (If not engineering, do you know whether that option is still realistically open to you?) Are you accepted to the Honors College?
Nobody here can tell, from what you’ve said, what the better choice would be; all we can do is pose questions that may help you and your family to figure that out for yourselves.